Certain delicate machines and scientific instruments can be rather sensitive to external vibrations. Generally there are two distinct effects--(1) high frequency vibrations which tend to excite a mechanical resonance in some part of the machine or its supports and (2) low frequency vibrations which tend to produce a non-resonant distortion of the machine's basic structure. Normally the former effect, at frequencies typically in the range of 100-1,000 Hz, can be effectively eliminated by the simple expedient of mounting the system on thin rubber pads. The latter effect, typically driven by building vibrations in the frequency range of 2-25 Hz, is much harder to eliminate and some sophisticated passive antivibration mounts have been developed for this purpose. It is these low frequency vibrations to which the present invention is directed.
The simplest method of vibration isolation consists of mounting the device to be isolated (or its platform) on a spring having a force constant .lambda.. To increase the energy absorption of a passive system, damping and compound spring devices have been employed. Although such passive systems can accomplish a great deal, some displacement of the device or platform results.
Consider the case of a passive mount consisting of a mass M supported on a spring of force constant .lambda., as illustrated in FIG. 1(a). Of interest is the vertical movement y.sub.1 of the mass M in response to a movement y.sub.2 of the supporting surface. If y.sub.2 is a harmonic displacement with angular frequency .omega. and amplitude a.sub.2, then the response y.sub.1 is also harmonic with amplitude a.sub.1 such that y.sub.1 =a.sub.1 e.sup.i.omega.t where i is the square root of -1. From this it is straightforward to show that: ##EQU1## At high frequencies the second term in the denominator is large and a.sub.1 therefore small, i.e. high frequency isolation is good. However, at a frequency .omega..sub.o given by EQU M.omega..sub.o.sup.2 /.lambda.=1
the amplitude a.sub.1 becomes infinite, and some damping must clearly be introduced in a practical device.
In the damped system of FIG. 1(b) having a damping factor .GAMMA., there is a viscous force F acting with amplitude F=.GAMMA..lambda..multidot.(d/dt)(y.sub.1 -y.sub.2). The response of the damped system is: ##EQU2## The amplitude a.sub.1 is now complex (i.e. phase shifted) but the amplitude at resonance is reduced to: ##EQU3## In practice the choice of damping factor .GAMMA. is a compromise between low resonant amplitude (equation 3) and sufficient high frequency isolation. Equation 2 shows that for the high values of .GAMMA. needed for low resonant amplitude, the amplitude a.sub.1 /a.sub.2 tends toward unity, i.e. no attenuation of the vibration amplitude. While more complex spring systems can offer better high frequency isolation, the problem of amplitude build up at resonance remains.
To overcome some of the shortcomings of a passive system various dynamic antivibration systems have been developed. Generically these systems detect the vibration and produce counter forces to cancel the forces driving the vibration. Such dynamic systems have been used to eliminate particular structural resonances (i.e. relatively high frequencies--the resonant condition referred to above). In such systems the correction forces have been derived using electric solenoids or compressed gas transducers.